The image shows a geometric figure consisting of two shapes: a triangle and a trapezoid.

Steps to find the perimeter:

The perimeter of a shape is the sum of the lengths of all its outer sides.

1. Sides of the triangle:
   The triangle has three sides:

   • One side of 5 cm,
   • One side of 6 cm,
   • One side of 4 cm.

2. Sides of the trapezoid:
   The trapezoid has four sides:

   • The upper base is 7 cm,
   • The lower base is 15 cm,
   • The two slanting sides are 6 cm and 8 cm.

Total Perimeter:

Now, we sum all the sides to get the perimeter: $\text{Perimeter} = 5 + 6 + 4 + 7 + 15 + 8 + 6 = 51 \, \text{cm}$

Thus, the perimeter of the combined shape is 51 cm.

Would you like further details on how to handle composite shapes like this? Here are 5 related questions to deepen your understanding:

1. How do you calculate the area of a trapezoid?
2. How do you find the area of the triangle in this composite shape?
3. What are the properties of trapezoids that differ from other quadrilaterals?
4. How can you determine if a shape is regular or irregular based on its side lengths?
5. How does knowing symmetry help in solving geometry problems?

Tip: When dealing with composite figures, break them into simpler parts (like triangles and trapezoids) to handle them more easily!